One of the most important themes of general relativity is the energy-momentum localization which
has no satisfactory solution. At present there is not an accepted definition of the localized
energy-momentum associated with the gravitational field. Nevertheless, several approaches have been
carried out to study the energy-momentum localization. A number of definitions for energy-momentum
complexes in general relativity have been given by many authors, including Einstein [1]},
Møller [2]}, Tolman [3]}, Papapetrou [4]}, Bergmann and Thomson [5]},
Landau and Lifshitz [6]}, and Weinberg [7]}. Energy-momentum complexes are
coordinate-dependent pseudotensorial quantities, except Møller, which can be used in quasi-Cartesian
coordinates, more precisely in Schwarzschild Cartesian coordinates [8]}, in Kerr-Schild Cartesian
coordinates [9]}, and in generalized Painlevé-Gullstrand Cartesian coordinates [10]}.
Yang et al. [11]} have shown that the energy component of the energy-momentum complexes
in Einstein prescription \(E_{\rm E}\)  and in Møller prescription \(E_{\rm M}\)  will be unlike beside
vacuum case \(T^0_0 = 0\)  earlier. Then, Vagenas [12]}, Matyjasek [13]} and Yang [10]}
attempt to find out the relation formula about \(E_{\rm E}\)  and \(E_{\rm M}\) . In this article, according
to the post-Newtonian approximation, I will study the difference between \(E_{\rm E}\)  and
\(E_{\rm M}\) , and their relationship.
